arXiv subjects

Murat Altunbulak

Publications and source records attributed to Murat Altunbulak.

4 recordsLinked to original sources

arXiv2026

On the permutation automorphisms of binary cubic codes

A binary linear code whose permutation automorphism group has a fixed point free permutation of order $3$ is called a binary cubic code. The scope of this paper is to investigate the structural properties of binary cubic codes. Let $C$ be a binary cubic $[n,k]$ code. In this paper, we prove that if $n\geq 30$ and $C$ has permutation automorphism group of order three, then $k\geq 6$. Additionally, we show that if $n < 30$ and $k\leq 4$, then the permutation automorphism group of $C$ has order greater than three. Moreover, along the way, we provide some results on the structure of the higher dimensional cubic codes. In particular, we present some results concerning the structure of the putative extremal self-dual $[72,36,16]$ code under the assumption that it is cubic.

cs.IT↗

arXiv2025

A toolbox of spin-adapted generalized Pauli constraints

We establish a toolbox for studying and applying spin-adapted generalized Pauli constraints (GPCs) in few-electron quantum systems. By exploiting the spin symmetry of realistic $N$-electron wave functions, the underlying one-body pure $N$-representability problem simplifies, allowing us to calculate the GPCs for larger system sizes than previously accessible. We then uncover and rigorously prove a superselection rule that highlights the significance of GPCs: whenever a spin-adapted GPC is (approximately) saturated - referred to as (quasi)pinning - the corresponding $N$-electron wave function assumes a simplified structure. Specifically, in a configuration interaction expansion based on natural orbitals only very specific spin configuration state functions may contribute. To assess the nontriviality of (quasi)pinning, we introduce a geometric measure that contrasts it with the (quasi)pinning induced by simple (spin-adapted) Pauli constraints. Applications to few-electron systems suggest that previously observed quasipinning largely stems from spin symmetries.

quant-ph↗

arXiv2023

On the binary linear constant weight codes and their autormorphism groups

We give a characterization for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. This characterization gives a correspondence between the set of binary linear constant weight codes and the set of partitions for the union of supports of the codewords. By using this correspondence, we present a formula for the order of the automorphism group of a binary linear constant weight code in terms of its parameters. This formula is a key step to determine more algebraic structures on constant weight codes with given parameters. Bonisoli [Bonisoli, A.: Every equidistant linear code is a sequence of dual Hamming codes. Ars Combinatoria 18, 181--186 (1984)] proves that the $q$-ary linear constant weight codes with the same parameters are equivalent (for the binary case permutation equivalent). We also give an alternative proof for Bonisoli's theorem by presenting an explicit permutation on symmetric difference of the supports of the codewords which gives the permutation equivalence between the binary linear constant weight codes.

cs.IT↗

arXiv2018

Generalized Pauli constraints in small atoms

The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systematic analysis. Early investigations have found evidence that these constraints are exactly saturated in several physically relevant systems, e.g., in a certain electronic state of the Beryllium atom. It has been suggested that in such cases, the constraints, rather than the details of the Hamiltonian, dictate the system's qualitative behaviour. Here, we revisit this question with state-of-the-art numerical methods for small atoms. We find that the constraints are, in fact, not exactly saturated, but that they lie much closer to the surface defined by the constraints than the geometry of the problem would suggest. While the results seem incompatible with the statement that the generalized Pauli constraints drive the behaviour of these systems, they suggest that the qualitatively correct wave-function expansions can in some systems already be obtained on the basis of a limited number of Slater determinants, which is in line with numerical evidence from quantum chemistry.

quant-ph↗